There is a lot of musicin the Primal Scream frontman. He shifts in his seat, dips his shoulders, wriggles his torso and moves as if he’s dancing to the rhythm of his words. He oozes music, drumming with his hands, singing snatches of riffs. “I love pop music,” he’ll say, tossing out snappy observations about recordings as diverse as The Archies’ Sugar, Sugar (“It makes me happy and it makes you dance. That’s pretty much what pop music’s supposed to do”) or the Eagles’ Lyin’ Eyes (“It’s beautiful but numb, like the Flying Burrito Brothers without the pain”). All the while, he’s trying to get to the essence of what moved Primal Scream to create the big, monstrous, mantra-like, psychedelic grooves of their mesmerising new album, More Light.

Gillespie enthuses about the Temptations and early Seventies Motown, “when there was a real kind of urban darkness in soul music”, and the joy of intense grooves. “A lot of music we love, funk, free jazz, James Brown, Fela Kuti, there’s a kind of constant pulse. It’s unrelenting, it keeps coming at you. And we all love Miles Davis’s electric period, early Yoko Ono, early Public Image Limited, just ferocious, high-energy, avant-garde rock ’n’ roll. We like to get one riff and stick with it. The tension never gets released. I find more freedom in modal music. I can think of hundreds of melodies, different ways of singing, different vocal inflections, words come up, fast imagery, fractured imagery, there’s no let up. I don’t know if it’s going to cause some sort of psychic concussion but it’s just what we do.”

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At 50, Gillespie still has the slender build and loose-limbed movement of his rock ’n’ roll youth, but beneath the fringe of floppy hair, his face is lined and worn, evidence that years as a poster boy for a hedonistic generation have left their mark. There was a time when he seemed volatile and perverse, projecting a stand-offish aura of danger and self-destruction, but now, “almost five years sober, off alcohol and drugs”, he comes across as sweet and smart, thoughtful, taking his time to digest questions and express his ideas in a soft Scottish accent.

“It put my life in chaos and caused me and everybody around me a lot of pain and difficulties,” he says of his years as a hard drug user. “I don’t want to get all American about this. It’s not for me to tell other people how to live their life. Most people can have a couple of drinks or lines and they might say the odd stupid thing or make a pass at somebody, but they don’t endanger their lives or put themselves in risky and humiliating situations. I just know that they are too powerful for me, and they change my personality for the worse. When you’re drinking and drugging you kind of shut yourself down. It wasn’t really about having a good time. With me and my friends, we were trying to obliterate ourselves. The band suffered creatively.”

Gillespie talks about other musicians who have been addicted to dangerous drugs, and points out you can always see the decline in their work. “Nobody beats the Class As.” Yet he is wary of being perceived as a hypocrite, or disowning his work, defending Primal Scream’s darkest, most nihilistic albums Vanishing Point (1997), XTRMNTR (2000) and the almost unlistenable noise of Evil Heat (2002) as “good art, ’cause it’s representative of the times and where we were at that point, paranoid and aggressive. But it had nowhere to go.”

More recent albums have shifted between their taste for deliberately dumb garage rock ’n’ roll (2007’s Riot City Blues) and minimalist grooves (2008’s Beautiful Future) without quite cohering into satisfying wholes. Since their 1987 debut Sonic Flower Groove, Primal Scream have been a group whose sense of rock history teeters on the edge of parody, yet they exhibit a bloody-minded commitment to experimentalism and creativity that has kept them going, and kept audiences tuning in, for 26 years and 10 albums.

“If there is a mission,” says Gillespie, “it’s a mission to try and express myself. People think it’s enough to have chords, melody, words and beat, but you’re trying to capture magic and writing a song is only the beginning of the process. When we started, I had this thing inside that I wanted to express but I didn’t know how to do it. We looked at debut albums by the Sex Pistols, Stooges, Velvets, Clash and Ramones, statement records that influenced and inspired a lot of people, and I thought: 'If you don’t do it on your first record, you’re finished.’ But we kept trying. We never made a great record till Screamadelica (1991) and, when that hit generationally, it was quite a thrill, but still I felt frustrated that I couldn’t express myself better. I wanted to make a record that was a representation of my reality, how I relate to art, what it means to me. I think it can be everything: you can have pop records that are experimental, or art records that are trashy rock ’n’ roll. You can have it all. I love it all, and I am trying to find ways to capture it all. I think you can become a better artist as you get older, that’s what I’m trying to say.”

Primal Scream in the early-Nineties

More Light should do much to restore Primal Scream’s reputation as one of the country’s most creative and ambitious rock bands. The music is dense yet uplifting, creating its own tensions with Gillespie’s dark, stream-of-consciousness lyrics. Songs like 2013, Culturecide, Tenement Kid and Walking With The Beast convey an impression of a highly strung, heartfelt assault on the inequities of the modern world, before building to the euphoric gospel release of closing track It’s Alright, It’s OK, on which Gillespie sings: “You can fix it once it’s been broken.” The Sun Ra Arkestra lend an off-kilter, jazzy wooziness to River Of Pain, and Robert Plant shudders and wails through Elimination Blues, which he sang face-to-face with Gillespie in the band’s small studio in Primrose Hill. “That was nice,” says Gillespie, of working with the Led Zeppelin frontman, then the fan in him breaks into an enormous grin. “It was better than nice, actually, it was f------ amazing!”

With More Light, it is as if Primal Scream have finally found a way to bring all the different strands of their musical obsessions together. The first record Gillespie has made completely sober, it still has a psychedelic sensibility, yet there is a depth to the sound and a tangible quality of compassionate humanity softening the hypnotic grooves.

“We are trying to create transcendent, euphoric, ecstatic experiences,” he insists. “That’s always going to be part of our aesthetic. We like making druggy-sounding psychedelic music. It’s just that since we stopped taking drugs we got better at it.”